Central Limit Theorem for Zero-Range Processes
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Bibliographic record
Abstract
We consider additive functionals t 0 V (s)ds of symmetric zero-range processes, where V is a mean zero local function. In dimensions 1 and 2 we obtain a central limit theorem for a -1 (t) t 0 V (s)ds with a(t) = t log t in d = 2 and a(t) = t 3/4 in d = 1 and an explicit form for the asymptotic variance 2 . The transient case d 3 can be handled by standard arguments [KV, SX,S]. We also obtain corresponding invariance principles. This generalizes results obtained by Port (see [CG]) for noninteracting random walks and Kipnis [K] for the symmetric simple exclusion process. Our main tools are the martingale method together with L 2 decay estimates [JLQY] for the process semigroup. 0 p t (0, 0)dt in d 3, where p t (x, y) are the transition probabilities of the corresponding continuous time random walk. The recurrence of the individual particles is responsible for the unusual scaling in one and two dimensions.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it